Proximal type methods for solving variational inequalities

We generalize the projection method for strongly monotone multivalued variational inequalities where the cost operator is not necessarily Lipschitz. At each iteration at most one projection onto the constrained set is needed. When the convex constrained set is not polyhedral we embed the proposed method in a polyhedral outer approximation that allows that the projection can be obtained by solving strongly convex quadratic programs with linear constraints.